Wireless cellular networks feature two emerging technological trends. The first is the direct Device-to-Device (D2D) communications, which enables direct links between the wireless devices that reutilize the cellular spectrum and radio interface. The second is that of Machine-Type Communications (MTC), where the objective is to attach a large number of low-rate low-power devices, termed Machine-Type Devices (MTDs) to the cellular network. MTDs pose new challenges to the cellular network, one if which is that the low transmission power can lead to outage problems for the cell-edge devices. Another issue imminent to MTC is the \emph{massive access} that can lead to overload of the radio interface. In this paper we explore the opportunity opened by D2D links for supporting MTDs, since it can be desirable to carry the MTC traffic not through direct links to a Base Station, but through a nearby relay. MTC is modeled as a fixed-rate traffic with an outage requirement. We propose two network-assisted D2D schemes that enable the cooperation between MTDs and standard cellular devices, thereby meeting the MTC outage requirements while maximizing the rate of the broadband services for the other devices. The proposed schemes apply the principles Opportunistic Interference Cancellation and the Cognitive Radio's underlaying. We show through analysis and numerical results the gains of the proposed schemes.